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Q. If two resistors of 4Ω and 6Ω are connected in series, what is the total resistance? (2023)

A. 10Ω
B. 24Ω
C. 2.4Ω
D. 12Ω

Solution

In series, R_eq = R1 + R2 = 4Ω + 6Ω = 10Ω.

Correct Answer: A — 10Ω

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Q. If x = 3, what is the value of 2x^2 - 5x + 1? (2022)

A. -2
B. 0
C. 4
D. 6

Solution

2(3^2) - 5(3) + 1 = 18 - 15 + 1 = 4.

Correct Answer: D — 6

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Q. If x = 5, what is the value of 2x + 3? (2022)

A. 10
B. 13
C. 8
D. 15

Solution

Substituting x = 5, we get 2(5) + 3 = 10 + 3 = 13.

Correct Answer: B — 13

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Q. If x = 5, what is the value of 3x + 2? (2022)

A. 17
B. 15
C. 20
D. 18

Solution

3(5) + 2 = 15 + 2 = 17.

Correct Answer: A — 17

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Q. If you have 0.25 moles of sulfuric acid (H2SO4), what is its mass? (2023)

A. 49 g
B. 98 g
C. 25 g
D. 12.5 g

Solution

Molar mass of H2SO4 = 2*1 + 32 + 4*16 = 98 g/mol. Mass = 0.25 moles x 98 g/mol = 24.5 g.

Correct Answer: B — 98 g

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Q. If z = -2 + 2i, what is the value of |z|? (2019)

A. 2√2
B. 4
C. 2
D. √2

Solution

|z| = √((-2)^2 + (2)^2) = √(4 + 4) = √8 = 2√2.

Correct Answer: A — 2√2

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Q. If z = 1 + i, what is the value of z^2? (2022)

A. 2i
B. 1 + 2i
C. 2
D. 0

Solution

z^2 = (1 + i)^2 = 1^2 + 2(1)(i) + i^2 = 1 + 2i - 1 = 2i.

Correct Answer: B — 1 + 2i

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Q. If z = 1 + i, what is the value of z²? (2022)

A. 0
B. 2i
C. 2
D. 1 + 2i

Solution

z² = (1 + i)² = 1² + 2(1)(i) + i² = 1 + 2i - 1 = 2i.

Correct Answer: D — 1 + 2i

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Q. If z = 2 + 2i, what is |z|^2? (2021)

A. 8
B. 4
C. 2
D. 0

Solution

|z|^2 = (2^2 + 2^2) = 4 + 4 = 8.

Correct Answer: A — 8

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Q. If z = 2 - 3i, what is the conjugate of z? (2020)

A. 2 + 3i
B. 2 - 3i
C. -2 + 3i
D. -2 - 3i

Solution

The conjugate of z = 2 - 3i is 2 + 3i.

Correct Answer: A — 2 + 3i

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Q. If z = 3 + 4i, what is the imaginary part of z? (2022) 2022

A. 3
B. 4
C. 7
D. 1

Solution

The imaginary part of the complex number z = 3 + 4i is 4.

Correct Answer: B — 4

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Q. If z = 3 + 4i, what is the value of z + z* (where z* is the conjugate of z)? (2017)

A. 6
B. 8
C. 12
D. 0

Solution

z + z* = (3 + 4i) + (3 - 4i) = 6.

Correct Answer: B — 8

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Q. If z = 3 + 4i, what is the value of z + z̅? (2022)

A. 6
B. 8
C. 7
D. 5

Solution

z + z̅ = (3 + 4i) + (3 - 4i) = 6.

Correct Answer: B — 8

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Q. If z = 4 + 3i, what is the real part of z? (2023)

A. 4
B. 3
C. 7
D. 1

Solution

The real part of the complex number z = 4 + 3i is 4.

Correct Answer: A — 4

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Q. If z = 5 + 12i, what is the argument of z? (2022)

A. arctan(12/5)
B. arctan(5/12)
C. π/2
D. 0

Solution

The argument of z = 5 + 12i is given by arctan(12/5).

Correct Answer: A — arctan(12/5)

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Q. If \( B = \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} \), what is \( |B| \)? (2022)

A. 5
B. 10
C. 1
D. 8

Solution

The determinant of \( B \) is \( 2*4 - 3*1 = 8 - 3 = 5 \).

Correct Answer: A — 5

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Q. In a buffer solution, which component resists changes in pH? (2020)

A. Strong acid
B. Weak acid and its salt
C. Strong base
D. Water

Solution

A buffer solution typically consists of a weak acid and its conjugate base (salt), which helps to resist changes in pH when small amounts of acid or base are added.

Correct Answer: B — Weak acid and its salt

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Q. In a Carnot engine operating between temperatures of 500 K and 300 K, what is the efficiency of the engine? (2023)

A. 40%
B. 50%
C. 60%
D. 70%

Solution

Efficiency (η) = 1 - (T_cold / T_hot) = 1 - (300 K / 500 K) = 0.4 or 40%.

Correct Answer: C — 60%

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Q. In a Carnot engine operating between temperatures T1 and T2, what is the efficiency (η) of the engine? (2023)

A. 1 - T2/T1
B. T1/T2
C. T2/T1
D. T1 - T2

Solution

The efficiency of a Carnot engine is given by η = 1 - T2/T1.

Correct Answer: A — 1 - T2/T1

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Q. In a Carnot engine, the efficiency depends on which of the following? (2023)

A. Temperature of the hot reservoir
B. Temperature of the cold reservoir
C. Both temperatures
D. Type of working substance

Solution

The efficiency of a Carnot engine is determined by the temperatures of the hot and cold reservoirs, given by the formula η = 1 - (T_c/T_h).

Correct Answer: C — Both temperatures

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Q. In a chemical reaction, what does the term 'activation energy' refer to? (2023)

A. Energy released during the reaction
B. Energy required to initiate the reaction
C. Energy needed to maintain the reaction
D. Energy that is lost

Solution

Activation energy is the minimum energy required to initiate a chemical reaction.

Correct Answer: B — Energy required to initiate the reaction

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Q. In a circuit with a 10Ω resistor and a 5V battery, what is the power consumed by the resistor? (2023)

A. 1W
B. 2W
C. 5W
D. 10W

Solution

Power P = V^2/R = 5^2/10 = 25/10 = 2.5W.

Correct Answer: B — 2W

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Q. In a circuit with a 15V battery and a 5Ω resistor, what is the voltage drop across the resistor? (2019)

A. 3V
B. 5V
C. 15V
D. 0V

Solution

The voltage drop across the resistor is equal to the battery voltage, which is 15V.

Correct Answer: C — 15V

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Q. In a circuit with a 24V battery and two 8Ω resistors in series, what is the total current? (2022)

A. 1A
B. 2A
C. 3A
D. 4A

Solution

Total resistance R = 8Ω + 8Ω = 16Ω. Current I = V/R = 24V / 16Ω = 1.5A.

Correct Answer: B — 2A

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Q. In a circuit with a 9V battery and a 3Ω resistor, what is the current flowing through the resistor? (2023)

A. 3A
B. 2A
C. 1A
D. 4A

Solution

Using Ohm's law, I = V/R = 9V / 3Ω = 3A.

Correct Answer: B — 2A

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Q. In a circuit with a 9V battery and a 3Ω resistor, what is the power dissipated by the resistor? (2021)

A. 3W
B. 9W
C. 6W
D. 12W

Solution

Power is given by P = V²/R = (9V)² / 3Ω = 81V² / 3Ω = 27W.

Correct Answer: B — 9W

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Q. In a circuit with a 9V battery and a 3Ω resistor, what is the power dissipated in the resistor? (2023)

A. 3W
B. 9W
C. 6W
D. 12W

Solution

Power P = V²/R = (9V)² / 3Ω = 81 / 3 = 27W.

Correct Answer: B — 9W

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Q. In a circuit with a voltage of 24V and a current of 6A, what is the resistance? (2020)

A. 2Ω
B. 4Ω
C. 6Ω
D. 8Ω

Solution

Using Ohm's Law, R = V/I = 24V / 6A = 4Ω.

Correct Answer: D — 8Ω

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Q. In a circuit, if the current is doubled while the resistance remains constant, what happens to the power consumed? (2020)

A. It doubles
B. It triples
C. It remains the same
D. It halves

Solution

Power is given by P = I²R. If I is doubled, P becomes (2I)²R = 4I²R, which means power quadruples.

Correct Answer: A — It doubles

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Q. In a circuit, if the resistance is doubled while the voltage remains constant, what happens to the current? (2021)

A. It doubles
B. It halves
C. It remains the same
D. It quadruples

Solution

According to Ohm's law, I = V/R. If R is doubled, I will be halved.

Correct Answer: B — It halves

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